Wavetronix v. EIS Electronic Integrated Systems

United States Court of Appeals for the Federal Circuit
2008-1129, -1160

WAVETRONIX,

Plaintiff-Appellant,

v.

EIS ELECTRONIC INTEGRATED SYSTEMS,

Defendant-Cross Appellant.

Brent P. Lorimer, Workman Nydegger, of Salt Lake City, Utah, argued for plaintiff-
appellant. With him on the brief were Thomas R. Vuksinick and David R. Todd. Of counsel
were Chad E. Nydegger and L. David Griffin.

Richard D. Rochford, Nixon Peabody LLP, of Rochester, New York, argued for
defendant-cross appellant. Of counsel on the brief were Michael F. Orman and Wendell W.
Harris.

Appealed from: United States District Court for the District of Utah

Senior Judge Bruce S. Jenkins
 United States Court of Appeals for the Federal Circuit

2008-1129, -1160

WAVETRONIX,

Plaintiff-Appellant,

v.

EIS ELECTRONIC INTEGRATED SYSTEMS,

Defendant-Cross Appellant.

Appeal from the United States District Court for the District of Utah in Case No. 2:05-
CV-73, Senior Judge Bruce Jenkins.
___________________________

DECIDED: July 29, 2009
___________________________

Before NEWMAN and SCHALL, Circuit Judges, and PATEL, District Judge. ∗

PATEL, District Judge.

Wavetronix LLC (“Wavetronix”) brought this patent infringement action against

EIS Electronic Integrated Systems (“EIS”). The patent in suit is United States Patent

No. 6,556,916 (“the ’916 patent”), entitled “System and Method for Identification of

Traffic Lane Positions.” Wavetronix and EIS both develop systems for monitoring the

∗
The Honorable Marilyn Hall Patel, United States District Court for the
Northern District of California, sitting by designation.
flow of automobile traffic on thoroughfares. Wavetronix accuses the automatic setup

feature of EIS’s Remote Traffic Microwave Sensor (“RTMS”) X3 monitoring device of

infringing one independent claim and several dependent claims of the ’916 patent,

literally or under the doctrine of equivalents.

The district court granted summary judgment of non-infringement to EIS.

Wavetronix appeals the judgment of non-infringement, and EIS cross-appeals dismissal

of its counterclaims of invalidity and unenforceability. We conclude that summary

judgment of non-infringement is proper, and we affirm the district court’s judgment. 1

I. BACKGROUND

A. The Patent in Suit and Its Technological Field

Urban planners require accurate counts of vehicular traffic in order to plan the

construction of new thoroughfares as well as to determine the optimal ways to use

existing thoroughfares. It is often useful to know how much traffic travels in a particular

lane, for instance a High-Occupancy Vehicle (HOV) lane, as compared to other lanes

on the same thoroughfare. Numerous sensor devices using, for example, radar or

acoustic signals have been developed to monitor the flow of vehicle traffic across

several lanes of a road or highway. The ’916 patent’s Figure 5 illustrates a roadside

sensor unit with a field of vision extending across several lanes of a street.

1
Wavetronix argues that there are legal and factual errors in the district
court’s opinion and that such errors warrant reversal. The existence of any such errors
does not, in itself, compel reversal. This court sits to review judgments, not opinions.
Stratoflex, Inc. v. Aeroquip Corp., 713 F.2d 1530, 1540 (Fed. Cir. 1983). The party that
prevailed below may defend a judgment on any ground which the law and record permit
that would not expand the relief it has been granted. United States v. N.Y. Tel. Co., 434
U.S. 159, 166 n.8 (1977).

2008-1129,-1160 2
 For these devices to accurately tally the number of vehicles traveling in each

lane, they must “know” where the lane boundaries are located. While a human being

can simply look at a highway and see where the lanes of traffic are located, a sensing

device must be “taught” the location of the lanes before it can begin to serve its

monitoring function. One way to achieve this is to allow the device to detect some

number of vehicles driving on the road and to extrapolate the locations of the lanes from

an examination of where the detected vehicles have actually tended to drive. The

underlying assumption (which highway patrol officers may dispute) is that drivers will

more often than not drive near the centers of lanes, rather than near or over lane

boundaries. If this assumption holds, then detecting where some number of vehicles

have actually been driven can assist in identifying the centers of lanes; likewise, the

2008-1129,-1160 3
places on the road on which automobiles have tended not to drive can be identified as

lane boundaries. The patent in suit is directed to a method of performing the initial step

of “teaching” a monitoring device the location of the traffic lanes on a given thoroughfare

using detection and observation of actual automobile traffic.

In 2000, Wavetronix undertook the development of a new radar-based traffic

monitoring system. Many of the prior art systems required manual adjustment to define

the locations of the traffic lanes on the highway to be monitored. Wavetronix sought to

improve the capability for automated lane definition. On September 27, 2001, three

inventors filed the application for what became the ’916 patent, naming Wavetronix as

the assignee. The patent issued on April 29, 2003. Only claim 1 is at issue on appeal. 2

That claim reads, in its entirety:

1. In a traffic monitoring system having a sensor, a method for defining
traffic lanes, comprising the steps of:
a. for a selectable plurality of vehicles,
i. detecting each of said selectable plurality of vehicles
present within a field of view of said sensor;
ii. estimating a position of said each of said selectable
plurality of vehicles;
iii. recording said position of said each of said selectable
plurality of vehicles;
b. generating a probability density function estimation from each of
said position of said each of said selectable plurality of vehicles;
and
c. defining said traffic lanes within said traffic monitoring system
from said probability density function estimation.

The specification discloses several preferred embodiments, all of which are described

through the use of histograms. Each of these histograms displays, in some form, a two-

2
Wavetronix has also accused EIS of infringing claims 2, 8, 9, 15 and 16.
Each of these is dependent upon claim 1’s limitations.

2008-1129,-1160 4
dimensional grid with peaks and valleys representing the relative heaviness of vehicle

traffic across a set of “range bins” representing spatial distances from the sensor.

These histograms, which are Figures 6, 7 and 8 in the patent, are shown below.

2008-1129,-1160 5
 The specification teaches that these histograms exemplify the kind of “probability

density function estimation” recited in steps (b) and (c) of claim 1, and that the “peaks of

the PDF represent the center of each lane and the low spots (or valleys) of the PDF

represent the lane boundaries (or regions where cars don’t drive).” ’916 patent col.6

ll.15-18. The specification also explains that statistical techniques are used to identify

the boundaries between lanes, and that these boundaries are then used to define the

lanes for the purpose of detecting where vehicles drive. See id. col.7 l.51-col.9 l.6.

2008-1129,-1160 6
 B. The Accused Device

As do prior art systems, EIS’s RTMS X3 detects and counts vehicles in several

lanes of a thoroughfare over an extended period of time. The initial determination of

lane locations may occur manually or may be assisted by the auto set-up feature of a

program called the “Setup Wizard.” It is this auto set-up feature of the RTMS X3’s

Setup Wizard that Wavetronix accuses of infringement. While the parties emphasize

different aspects of the system, there is no material dispute of fact as to how the

accused system operates.

The RTMS X3 sensor unit, or transceiver, has a field of view that extends across

a given roadway. The field of view is divided into thirty-two “range slices,” each having

a width of about three meters, i.e., the approximate width of a normal traffic lane. The

transceiver is attached to a pole alongside the road, and a human installer connects the

transceiver to a laptop computer. The transceiver detects passing automobiles, and a

graphic on the computer screen displays small images to represent them. The system

cannot accurately assign any particular automobile to a lane until range slices are

matched up with actual lanes in the transceiver’s field of vision. The human installer

may define lanes manually by aligning the lane boundaries on the computer’s screen

with the spaces between blips displayed on the laptop that represent passing

automobiles. Alternatively, the installer may choose to use the Setup Wizard’s auto set-

up feature. If this feature is chosen, the installer tells the RTMS X3 how many lanes to

expect. The RTMS X3 then monitors and records automotive traffic for one minute. 3

3
Naturally, this process will not work on an empty road but must rather be
used at a time and place in which it may be expected that a significant number of
automobiles will pass through the lanes on the road.

2008-1129,-1160 7
 During that one minute, the transceiver continuously transmits radar signals

toward the roadway and detects the reflected signals, while the Setup Wizard processes

the data so generated in several steps. First, every ten milliseconds the system

generates a series of thirty-two numbers corresponding to the strength of the reflected

radar signal in each of the thirty-two range slices. A processor independently compares

each of the thirty-two values to a particular “detection threshold.” The results of this

comparison are stored in a thirty-two position array, i.e., a sequence of thirty-two

locations in the transceiver’s memory called the “Q-vector.” The Q-vector stores, for

each range slice, the difference between its reflected radar strength and the detection

threshold. Only if an automobile has driven in a particular range slice within the

preceding ten milliseconds will the Q-vector contain a positive value corresponding to

the position of that range slice. The values in the Q-vector are replaced every ten

milliseconds as new signal measurements are taken by the sensor. During the one-

minute set-up process, the contents of the Q-vector array are continuously sent to the

laptop, where they are replicated in an array called the “REQ array.” The REQ array

processes only about twenty percent of the Q-vector data that is generated, because

the transceiver generates data faster than it can be transmitted to the laptop.

As data is sent to the laptop’s REQ array, the Setup Wizard software identifies

“local maxima” for each ten-millisecond increment of time. A local maximum is

identified when the value at a particular position in the thirty-two position REQ array is

greater than the values at the positions to the immediate left or right. After identifying all

of the local maxima present in the REQ array during a given ten-millisecond interval, the

Setup Wizard software ignores everything except the “first” local maximum, which is the

2008-1129,-1160 8
local maximum nearest to the sensor. The various stages of processing so far

described result in the production of one “first local maximum” corresponding to one of

the thirty-two range bins every ten milliseconds.

The next step involves an array called the “NAMP array.” Wavetronix contends

that it is the NAMP array that “generat[es] a probability density function estimation” as

described in claim 1, step (b), of the ’916 patent. As a first local maximum is produced

every ten milliseconds, the NAMP array, which like the other arrays has thirty-two

positions, adds up the number of first local maxima per position over the course of the

one-minute set-up period. The system records first local maxima, not discrete

automobiles. Unless an automobile is exceedingly fast or small, it is likely to produce

multiple first local maxima when passing through the sensor’s field of vision. The

following illustrations depict two notional automobiles driving through the RTMS X3 field

of vision. Only five range slices, numbered 0 through 4, are depicted. Range slices 1-3

correspond to lanes, while range slices 0 and 4 correspond to shoulders. As each

automobile drives through the field of vision in a given lane, a number of first local

maxima register in the NAMP array. 4

4
These illustrations, taken from Wavetronix’s principal brief, describe the
graph on the right of each illustration as a “NAMP Array Histogram.” The court does not
necessarily adopt the description of the NAMP array as a “histogram.”

2008-1129,-1160 9
2008-1129,-1160 10
 As noted, the RTMX X3’s field of vision actually contains thirty-two range slices,

not just five. Upon completion of the one minute period, the NAMP array contains thirty-

two values corresponding to each of the thirty-two range slices. These NAMP array

values are used to define lanes. Specifically, the Setup Wizard defines as a lane any

range slice for which the final count in the NAMP array exceeds about one percent of

the total number of Q-vectors analyzed in the laptop. Because the set-up period lasts

about one minute, a given range slice must register a minimum of approximately ten

counts in order for the system to determine that the range slice corresponds to a lane.

2008-1129,-1160 11
A range slice is either found to correspond to a lane or it is not. If fewer lanes are found

than the human installer told the system to expect, then the one-minute detection and

recording stage repeats itself. If more lanes have been found than expected, the

system deletes the lanes that registered the least number of first local maxima until the

expected number of lanes is reached. Upon completion of the set-up phase, the Setup

Wizard has identified which of the thirty-two range slices spanning the sensor’s field of

vision actually correspond to traffic lanes. The system is then ready to begin the long-

term monitoring of vehicle traffic within the identified lanes.

C. Relevant Procedural History

Wavetronix filed this action on January 27, 2005. On March 13, 2006, the district

court granted summary judgment to Wavetronix on EIS’s best mode defense, finding as

a matter of law that EIS could not prevail on the defense. The district court similarly

granted summary judgment to Wavetronix on EIS’s inequitable conduct defense, on

May 18, 2006. The court conducted some fourteen days of pre-trial hearings and, on

September 21, 2007, entered an order granting summary judgment of non-infringement.

At no time did the court enter a claim construction order. After entry of judgment

dismissing Wavetronix’s claim of infringement and EIS’s counterclaims of invalidity and

unenforceability, Wavetronix timely appealed and EIS timely cross-appealed. We have

jurisdiction pursuant to 28 U.S.C. § 1295(a)(1).

II. DISCUSSION

The appeal and cross-appeal are taken from judgment entered by the district

court following grants of summary judgment. A court may grant summary judgment only

when, drawing all inferences and resolving all doubts in favor of the non-moving party,

2008-1129,-1160 12
there are no genuine issues of material fact and the moving party is entitled to judgment

as a matter of law. Fed. R. Civ. P. 56(c). See generally Anderson v. Liberty Lobby,

Inc., 477 U.S. 242 (1986). A fact is “material” if it may affect the outcome of the

proceedings, and an issue of material fact is “genuine” if the evidence is such that a

reasonable jury could return a verdict for the non-moving party. Anderson, 477 U.S. at

248. The moving party bears the burden of identifying those portions of the pleadings,

discovery and affidavits that demonstrate the absence of a genuine issue of material

fact. Celotex Corp. v. Catrett, 477 U.S. 317, 323 (1986). Once the moving party meets

its initial burden, the non-moving party must go beyond the pleadings and, by its own

affidavits or discovery, set forth specific facts showing that there is a genuine issue for

trial. Fed R. Civ. P. 56(e); see Anderson, 477 U.S. at 250. We review a district court’s

grant of summary judgment de novo. Netscape Commc’ns Corp. v. Konrad, 295 F.3d

1315, 1319 (Fed. Cir. 2002).

A. Claim Construction

The district court determined as a matter of law that the EIS system does not

infringe the ’916 patent. Infringement analysis involves a two-step process: the court

first determines the meaning of disputed claim terms and then compares the accused

device to the claims as construed. Markman v. Westview Instruments, Inc., 52 F.3d

967, 976 (Fed. Cir. 1995), aff’d, 517 U.S. 370 (1996); see also Middleton, Inc. v. Minn.

Mining & Mfg. Co., 311 F.3d 1384, 1387 (Fed. Cir. 2002).

The district court did not explicitly construe claim 1’s “probability density function

estimation” limitation. The parties agree that this is the only claim term requiring

construction. They urge this court to construe the term on appeal rather than remand

2008-1129,-1160 13
for claim construction. There being only one independent claim in dispute and no

material issues of fact as to how the accused system works, the construction of that

term is the key issue for deciding infringement.

Although claim construction is a question of law, we generally refuse to construe

claims in the first instance. See, e.g., Metro. Life Ins. Co. v. Bancorp Servs., L.L.C., 527

F.3d 1330, 1336 (Fed. Cir. 2008); Electro Scientific Indus., Inc. v. Dynamic Details, Inc.,

307 F.3d 1343, 1350 (Fed. Cir. 2002); Bayer AG v. Biovail Corp., 279 F.3d 1340, 1349

(Fed. Cir. 2002). But see Frank’s Casing Crew & Rental Tools, Inc. v. PMR Techs.,

Ltd., 292 F.3d 1363, 1373 (Fed. Cir. 2002). We have explained that this court’s review,

although de novo, is not to function as an independent analysis in the first instance.

See Nazomi Commc’ns, Inc. v. Arm Holdings, PLC, 403 F.3d 1364, 1371 (Fed. Cir.

2005). In this case, however, we accept the parties’ invitation to construe the

“probability density function estimation” claim term, for three reasons. First, although

the district court did not specifically construe the claim term, its opinion references the

question of claim construction, and it is apparent that the district court’s views on the

matter have been exhausted. See id. (noting importance of taking into account views of

trial judge); see also Fireman’s Fund Ins. Co. v. United States, 909 F.2d 495, 499 (Fed.

Cir. 1990) (addressing new argument in first instance where remand would serve no

useful purpose). Second, both parties have agreed that we should construe the claim

limitation. Third, we agree that the record, which includes considerable evidence and

expert testimony, has been sufficiently developed to enable us to construe the claim

term without prejudicing either party. See Fireman’s Fund, 909 F.2d at 499; cf. Apex,

Inc. v. Raritan Computer, Inc., 325 F.3d 1364, 1374-75 (Fed. Cir. 2003) (declining to

2008-1129,-1160 14
construe claim terms where record had not been sufficiently developed, because

prejudice could result).

A claim term is construed according to its ordinary and customary meaning as

understood by a person of ordinary skill in the art at the time of the invention. Phillips v.

AWH Corp., 415 F.3d 1303, 1312-13 (Fed. Cir. 2005) (en banc). 5 “[T]he court looks to

those sources available to the public that show what a person of skill in the art would

have understood disputed claim language to mean,” including “the words of the claims

themselves, the remainder of the specification, the prosecution history, and extrinsic

evidence concerning relevant scientific principles, the meaning of technical terms, and

the state of the art.” Id. at 1314 (citations and internal quotation marks omitted). A

dictionary definition may be relied upon “so long as [it] does not contradict any definition

found in or ascertained by a reading of the patent documents.” Id. at 1322-23 (quoting

Vitronics Corp. v. Conceptronic, Inc., 90 F.3d 1576, 1584 n.6 (Fed. Cir. 1996)).

There is no dispute that a “probability density function estimation” (“PDFE”) is, in

some manner, an “estimation” of a “probability density function” (“PDF”). In the words of

Wavetronix’s expert, “probability density function is a precisely defined term in statistics

which corresponds to the probabilities of the different possible outcomes of some

experiment.” EIS agrees that “PDF” is a well known mathematics term and offers the

following dictionary definition: “a function of a continuous variable whose integral over a

region gives the probability that a random variable falls within the region.” 6 While the

5
Neither party has argued that the other party’s proffered experts are
unqualified to opine as persons of ordinary skill in the art.
6
Random House Webster’s Unabridged Dictionary 1541 (2d ed. 2001).
This definition comports with those found in other general reference and technical

2008-1129,-1160 15
parties agree upon the definition of “PDF,” they dispute the definition of “PDFE.” We

conclude below that the salient difference between the two concepts is that a PDF is a

mathematical function, whereas a PDFE is an approximation of such a function using

actual finite data. We also explain below that, in light of the teachings of the

specification and the recitation of the PDFE within the claim language, for the purposes

of claim 1 a PDFE must estimate a PDF with sufficient precision to indicate both where

vehicles are located and where they are not. In other words, as the specification

teaches, a PDFE should at a minimum provide enough data to ascertain “peaks” and

“valleys” approximating the centers and boundaries of traffic lanes, respectively.

In advocating for its construction of “PDFE,” EIS focuses on the term “probability”

and argues that a PDFE must represent some sort of probabilistic analysis. Wavetronix

argues that the “E” in “PDFE” modifies the whole phrase “PDF,” not just “P” or

“probability.” According to Wavetronix, an “estimate” of a PDF need not have all of the

characteristics of an actual PDF, including estimating the actual probability that a

vehicle has driven in a given lane. Rather, as we understand Wavetonix’s argument,

any histogram that allows for an estimation of lane boundaries is a PDFE, because any

graph that accurately allows for lane detection must have some correlation with the

number or probability of cars in each lane. Wavetronix argues that the definition that

most aligns with the specification and includes all of the disclosed embodiments is “a

tabulation of frequencies of vehicle positions.”

dictionaries. See, e.g., Webster’s Third New International Dictionary 1806 (2002) (“a
function of a continuous random variable whose integral over an interval gives the
probability that its value will fall within the interval”); McGraw-Hill Dictionary of Scientific
and Technical Terms 1674 (6th ed. 2003) (“[a] real-valued function whose integral over
any set gives the probability that a random variable has values in this set”).

2008-1129,-1160 16
 The claim language itself provides little guidance on how to define “PDFE,” and

the parties have not relied upon the patent’s prosecution history to define the proper

scope of the claim limitations referencing a PDFE. 7 The patent’s specification does

provide guidance, but its references to PDFE are not entirely consistent. Nowhere does

the patent set forth an explicit definition of PDFE. See Phillips, 415 F.3d at 1316

(patentee may act as own lexicographer); Johnson Worldwide Assocs., Inc. v. Zebco

Corp., 175 F.3d 985, 990 (Fed. Cir. 1999) (same). The specification refers variously to:

a PDF “as estimated,” ’916 patent col.6 l.6; using a PDF “to estimate” lane boundaries,

id. col.6 ll.14-15; “PDF estimation,” id. col.6 l.32; a “PDF estimator,” id. col.6 l.33; and

“estimated PDFs,” id. col.8 l.13. In some places, the specification appears to refer to

PDF and PDFE interchangeably. Id. col.4 ll.1-7, col.7 ll.30-39.

The concept of “PDF” is defined with greater clarity and consistency in the

specification than is the concept of “PDFE” standing alone. Both the summary of the

invention and the description of the preferred embodiments describe the concept of

PDF in terms of a graph in which enough data is collected to observe peaks, which

7
The parties look to the patent’s prosecution history only for the purposes
of supporting their respective positions on the question of whether claim 1 requires the
counting of discrete vehicles. EIS points out that Wavetronix remained silent in the face
of the patent examiner’s characterization of the patent’s method as “determining . . . the
number of cars which pass beneath [the sensor].” According to EIS, Wavetronix
conceded through its silence that the patent claimed the counting of discrete vehicles as
opposed to mere vehicle detections that may or may not yield an accurate tally of
individual vehicles. The parties have expended considerable effort arguing this point.
Whatever the merits of the argument, see 3M Innovative Props. Co. v. Avery Dennison
Corp., 350 F.3d 1365, 1373-74 (Fed. Cir. 2003) (silence does not necessarily indicate
acquiescence to examiner’s characterization when allowance is on grounds unrelated to
characterization), it is unnecessary to decide whether the claim encompasses only
detections of discrete vehicles. Even if the claim also encompasses vehicle detections,
an accused system must still generate a PDFE and define lanes from said PDFE to
infringe. For the same reason, it is also unnecessary to determine whether a PDFE
requires “unbiased” or “normalized” data, as asserted by EIS.

2008-1129,-1160 17
represent the centers of lanes, and valleys, which represent the lane boundaries or

edges. See, e.g., id. col.4 ll.2-7 (summary of invention) (“The probability density

function describes the probability that a vehicle will be located at any range. The peaks

of the probability function represent the center of each lane and the valleys of the

probability density function represent the lane boundaries.”); id. col.6 ll.15-19

(explanation of Figure 3, a diagram of the method) (“The peaks of the PDF represent

the center of each lane and the low spots (or valleys) of the PDF represent the lane

boundaries (or regions where cars don’t drive). The lane boundaries are set to be the

low spots (or valleys) between peaks.”). This “peaks and valleys” arrangement allows

for the definition of lanes from the PDFE as recited in step (c) of claim 1.

The understanding of PDF as a data plot showing a range of high values

(“peaks”) and low values (“valleys”) as explicated in the specification aligns well with the

standard mathematics definition of PDF. A PDF is a theoretical mathematical function

that seeks to model reality. As Wavetronix’s expert noted, a PDF does not represent

actual data. When displayed on a histogram, a PDF is a smooth line or curve, because

it is produced by a mathematical equation. When a finite set of actual data is plotted on

a histogram, the resulting plot will not be a smooth curve but rather a disjointed one.

See, e.g., ’916 patent fig.8. Such a plot may be represented by points connected with

lines or by a series of bars. The more data that is collected and plotted, the smoother

the line will be; however, a plot based on data would require an infinite number of data

points to duplicate the perfect smoothness of a mathematical function. In real-world

situations such as traffic monitoring, it is impossible to collect infinite data, but a plot of a

significant number of automobiles can estimate the mathematical curve that would

2008-1129,-1160 18
describe the automobiles’ distribution. A PDF and a PDFE do not, therefore, differ in

the sense of allowing for a comparison of values over a range of positions. The

distinction between them lies, rather, in the fact that a PDF is a perfectly smooth

mathematical function, whereas a PDFE is an estimation of some hypothetical PDF.

The PDFE is not perfectly smooth, but it has the advantage of being based on actual

data.

The specification is hardly a paragon of clarity, but this understanding of PDF

estimation comports with the various descriptions and explanations of the PDF and

PDFE concepts found in the specification. There are differences between the

embodiments disclosed in the specification, but each of them suggests that a number of

data points is used to estimate a hypothetical mathematical model, i.e., a PDF. One

embodiment (shown in the histogram at Figure 7) uses “normalized” data, i.e., data

displayed as a percentage of a total rather than as raw counts, while at least one

(shown in the histogram at Figure 8) does not. 8 Two embodiments apparently refer to a

count of individual vehicles (Figures 6 and 8), see ’916 patent col.7 l.25 (“The number of

vehicles in each bin is counted . . . .”), while a third (Figure 7) could just as easily refer

to vehicle detections, i.e., the number of signals bounced back to the transceiver, which

may be more than one per vehicle. What is the same about all of the disclosed

embodiments (Figures 6, 7 and 8) is that each of them represents, in the form of a

histogram, a comparison of the number of vehicles or vehicle detections across a range.

8
That Figure 7 represents a normalized graph is indicated by the fact that
the y-axis is scaled from zero to one. A given value is expressed as a fraction of the
whole, rather than as a raw count of detections. Determining the fraction of the whole
represented by a given value in Figure 8, which is not normalized, would require
dividing that value by the total number of counts measured in all positions.

2008-1129,-1160 19
This ability to compare the data across a range is significant, because it provides

information not only about where vehicles are but where they are not—i.e., where traffic

lanes begin and end. 9 Such data is used for “defining . . . traffic lanes . . . from said

[PDFE].” The record reveals no material intrinsic or extrinsic evidence indicating that

the attribute of a PDF that a PDFE does not possess is the fundamental property of

functioning over a range.

In summary, what makes a PDFE an estimate of a PDF in the context of the ’916

patent is the fact that a PDFE is based on actual data points, rather than a perfectly

smooth, if hypothetical, mathematical function or model. But a PDFE, like a PDF, has

the characteristic of comparing values across a range of positions. The court therefore

construes a PDFE to be “a finite data set large enough to approximate a function of a

continuous variable whose integral over a region gives the probability that a random

variable falls within the region.” This construction applies equally to step (b)

(“generating a [PDFE] . . .”) and step (c) (“defining . . . traffic lanes . . . from said

[PDFE]”) of claim 1; however, our infringement analysis infra focuses on step (c).

9
The patent contains two references suggesting that some embodiments
may have only one range bin per lane. See ’916 patent col.7 ll.7-8 (“[A] lane may be
comprised of a plurality of bins) (emphasis added); id. col.9 ll.58-61 (a limitation in claim
3 claiming a plurality of range bins in each lane, which appears redundant if claim 1
already implies this limitation). No doubt, using one bin per lane would not result in an
optimal lane definition using the “peaks” and “valleys” method. Nevertheless, there is
nothing plainly suggesting that, if only one bin per lane were used, the method would
take advantage of some technique other than comparing values across a range of lanes
to define lanes. The specification teaches that range bins of a width that results in
histograms without “peaks” and “valleys” are incapable of providing useful information
about where vehicle lanes begin and end. This teaching is an essential characteristic of
the patented system, and is relevant to the analysis of both literal infringement and
infringement under the doctrine of equivalents.

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 B. Literal Infringement

Aided by our construction of PDFE, we now turn to the question of literal

infringement. “Literal infringement of a properly construed claim is a question of fact.”

Applied Med. Res. Corp. v. U.S. Surgical Corp., 448 F.3d 1324, 1332 (Fed. Cir. 2006).

“We affirm a district court’s grant of summary judgment of non-infringement only if, after

viewing the alleged facts in the light most favorable to the non-movant, there is no

genuine issue as to whether the accused device is encompassed by the claims.”

Combined Sys., Inc. v. Def. Tech. Corp. of Am., 350 F.3d 1207, 1210 (Fed. Cir. 2003)

(citation omitted).

Wavetronix contends that the RTMS X3 Setup Wizard uses the NAMP array data

to perform the step of “defining . . . traffic lanes” as set forth in step (c) of claim 1.

Wavetronix characterizes the operation of the Setup Wizard software as using

detections of first local maxima to conclude “it is probable” vehicles travel in certain

range slices. EIS counters that the accused device performs no probability analysis,

and indeed that no such probability analysis could be performed using the NAMP array.

While the NAMP array collects data for a number of bins corresponding to spatial

positions, these data cannot fairly be said to represent probabilities. EIS states that its

device never conducts any probabilistic analysis to search for “peaks” and “valleys” in a

histogram, wherein valleys would represent boundaries between the lanes. Rather,

because the EIS system uses bins that are the full width of normal traffic lanes, the data

collected in the NAMP array is simply too coarse to reveal any “peaks” representing

lane centers or any “valleys” representing lane boundaries. EIS argues that its system

actually employs a much simpler methodology that identifies traffic lanes by applying a

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common threshold value to the NAMP data. EIS also notes that the system requires

manual intervention by a human to set the precise boundaries of traffic lanes. Because

the NAMP array does not have any of the essential properties of the PDFEs described

in the ’916 patent, EIS argues that its system cannot meet the “defining said traffic lanes

. . . from said [PDFE]” limitation, either literally or by equivalents.

Properly construed, the PDFE claim term requires a representation of vehicle

frequencies across a range of positions with sufficient detail to provide meaningful

information about where traffic lanes begin and end. This detail allows for the definition

of lanes claimed in step (c). In contrast, the processing of the sensor data in the NAMP

array, which the parties agree is used to select lanes, does not involve comparisons

among values for the range slices. As noted, the parties are in agreement as to how

the accused system operates. In the words of Wavetronix’s brief, “[T]he Wizard defines

a lane as any range slice for which the final count in the NAMP array exceeds about

one percent of the total number of Q-vectors analyzed in the laptop.” The analysis of

the NAMP array data does not involve comparisons across lanes using “peaks” and

“valleys” or any similar method. The determination that any particular range slice

corresponds to a lane is made independently for each range slice, without reference to

the values in other range slices. In other words, the range of highs and lows in the

NAMP array does not provide data from which the user could extrapolate lane

boundaries. Thus, the character of the NAMP data does not comport with our

previously stated construction of PDFE.

As an example, imagine a four-lane highway, and imagine further that the NAMP

array values collected for the four lanes are x, x-1, x+2 and x+1, in that order. The fact

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that x+2 is the highest value (and could accordingly be described as a “peak”) and that

x-1 is the lowest value (and could be described as a “valley”) is irrelevant to the

definition of traffic lanes. There is only one value per lane; therefore, both the “peak”

and the “valley” represent whole lanes, rather than lane centers or boundaries. This

illustrates that the data set produced in the NAMP array is too coarse to be a PDFE in

the sense required by the ’916 patent. The RTMS X3 selects lanes by analyzing the

NAMP array data, and the NAMP array cannot be a PDFE. Accordingly, we hold as a

matter of law the RTMS X3 does not practice the “defining . . . traffic lanes” step of claim

1 and therefore does not literally infringe the ’916 patent.

C. Doctrine of Equivalents

Wavetronix argues that the district court failed to give adequate consideration to

the possibility of infringement by equivalents. EIS contends that Wavetronix waived the

argument below. We assume without deciding that Wavetronix did not waive the

argument.

The essential inquiry under the doctrine of equivalents is whether “the accused

product or process contain[s] elements identical or equivalent to each claimed element

of the patented invention.” Warner-Jenkinson Co., Inc. v. Hilton Davis Chem. Co., 520

U.S. 17, 40 (1997). As with literal infringement, infringement by equivalents is a

question of fact. Id. at 38. “An element in the accused product is equivalent to a claim

limitation if the differences between the two are ‘insubstantial’ to one of ordinary skill in

the art.” Eagle Comtronics, Inc. v. Arrow Commc’n Labs., Inc., 305 F.3d 1303, 1315

(Fed. Cir. 2002) (citing Warner-Jenkinson, 520 U.S. at 40); see also Graver Tank & Mfg.

Co. v. Linde Air Prods. Co., 339 U.S. 605, 609 (1950). A plaintiff can prove equivalence

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by showing on a limitation-by-limitation basis that the accused product performs

substantially the same function in substantially the same way with substantially the

same result as each claim limitation of the patented product. Eagle Comtronics, 305

F.3d at 1315 (quoting Graver Tank, 339 U.S. at 608); see also Warner-Jenkinson,

520 U.S. at 39-40. A court may not apply the doctrine of equivalents where so doing

would effectively eliminate a claim element in its entirety. Warner-Jenkinson, 520 U.S.

at 29; Carnegie Mellon Univ. v. Hoffmann-La Roche, Inc., 541 F.3d 1115, 1129 (Fed.

Cir. 2008).

The Setup Wizard does not define lanes in substantially the same way as the

patented method because it simply confirms whether the range slices of uniform width

set in the system by the operator are aligned with actual traffic lanes on a one-to-one

basis. Indeed, the Setup Wizard’s determination of where lanes are located is made in

relation to a specific threshold, rather than as a comparison between different range

slices. The significance of this difference may be illustrated by returning to the example

of the series of four hypothetical NAMP array values x, x-1, x+2 and x+1. If the

threshold value were, for example, x-3, then all four of the values would be determined

by the EIS system to represent lanes, regardless of any “peak” or “valley,” because they

all exceed the threshold. If, on the other hand, the threshold value were x+3, then none

of the values would be determined to represent lanes. 10 The “peaks” and “valleys” that

are so critical to the method of the ’916 patent are irrelevant to the way the Setup

Wizard uses data to select lanes. Claim 1 of the ’916 patent requires the definition of

10
To put it another way, the integral over a given NAMP region does not
indicate the probability a vehicle has driven within that region, as is required by our
construction of PDFE.

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lane boundaries by analyzing vehicle traffic both among and within lanes to determine

where cars are actually driving, which as a matter of probability should reveal the

centers of the lanes. In contrast to the ’916 patent’s definition of traffic lanes from a

PDFE, none of the operations on or by the Q-vector, REQ array or NAMP array use any

meaningful information about where traffic lanes begin and end to accomplish lane

selection. The system can use the data only to confirm whether a range slice that is

already pre-selected to be the full width of a traffic lane is or is not within the trafficked

roadway—it does not compare data across different bins to locate the boundaries

between lanes. Assuming arguendo that the EIS system can be said to “define” traffic

lanes, it does so in a very different way than the way taught by the ’916 patent. It

cannot be said that these differences are insubstantial.

Wavetronix has focused exclusively on the NAMP array as the step in EIS’s

process that purportedly generates a PDFE from which lanes are defined. Data is

processed using several arrays, however. In the context of a patent in the mechanical

arts, we have noted: “[T]wo physical components of an accused device may be viewed

in combination to serve as an equivalent of one element of a claimed invention, as long

as no claim limitation is thereby wholly vitiated.” Searfoss v. Pioneer Consol. Corp., 374

F.3d 1142, 1151 (Fed. Cir. 2004) (alteration in original) (quoting Ethicon Endo-Surgery,

Inc. v. U.S. Surgical Corp., 149 F.3d 1309, 1320 (Fed. Cir. 1998)). If the data

associated with some other array could be described as a PDFE, it could be argued that

the combination of that array and the NAMP array infringes the “defining . . . traffic

lanes” step by equivalents. As noted above, some comparisons across lanes are made

in relation to the REQ array to the extent that a local maximum is defined at any array

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position having a higher value than do the positions to its immediate left or right. This

suggests that the operations carried out with the REQ array could perhaps be

expressed in terms of PDFEs. Conceivably, expert testimony on remand might

establish that each of these repeated comparisons across a few range slices

approximates a function of a continuous variable whose integral over that limited region

gives the probability that some random variable falls within the region, as required by

our construction of “PDFE.”

Even so, there would be no infringement by equivalents. Even if these

comparisons within the REQ array were determined to be PDFEs, the “way” in which

the combination of the REQ array and the NAMP array defines lanes—assuming the

EIS system “defines” lanes at all, in the sense of the ’916 patent—is much different.

During the one minute set-up period, a multitude of comparisons are made in the REQ

array to generate the NAMP data that is used to define lanes by applying a threshold.

Neither claim 1 nor the specification foresees the use of a multiplicity of PDFEs to

define lanes. The claim language describes defining lanes from “said” PDFE, and every

embodiment in the specification teaches the use of a method that can be described by a

single PDFE. This problem notwithstanding and as noted above, the RTMS X3 does

not assist in the identification of traffic lane boundaries: it can only use the data it

collects to confirm whether a range slice that is already pre-selected to be the full width

of a traffic lane is or is not within the trafficked roadway. Accordingly, even if the

combination of the NAMP array and the REQ array could be said to “defin[e] . . . said

traffic lanes . . . from said [PDFE]”—and it cannot—it would still do so in a very different

way than the patented invention. For these reasons, looking beyond the NAMP array

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would not salvage Wavetronix’s infringement case. There is as a matter of law no

infringement by equivalents.

D. Cross-Appeal

The district court determined on summary judgment that EIS could not prevail on

its inequitable conduct and best mode counterclaims. EIS has cross-appealed these

two rulings. Having considered the cross-appeal, we affirm the district court’s grant of

summary judgment on the counterclaims.

III. CONCLUSION

We agree with the district court, albeit on different grounds, that as a matter of

law the RTMS X3 does not infringe claim 1 of the ’916 patent. We also agree that

defendant-cross appellant’s counterclaims should be dismissed.

AFFIRMED.

COSTS

Each party shall bear its own costs on appeal.

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